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# Chapter 7

### The Quantum-Mechanical Model of the Atom

TermDefinition
Quantum-Mechanical Model of an Atom A model that explains the strange behavior of electrons
Electromagnetic Radiation A type of energy embodied in oscillating electric and magnetic fields...Ex: Light
Magnetic Field A region of space where a magnetic particle experiences a force
Electric Field A region of space where an electrically charged particle experiences a force
Amplitude The vertical height of a crest(or depth of a trough). Amplitude determines the light's intensity or brightness. The greater the amplitude, the greater the brightness
Wavelength(lambda symbol) The distance between adjacent crests(or any two analogous points). Determines color of light. Measured in units such as meters, micrometers, or nanometers. Short wavelengths = high energy....Large wavelength = low energy
Most Energetic Wave The most energetic waves have large amplitudes and short wavelengths
Frequency(v) The number of cycles(or wave crests) that pass through a stationary point in a given period of time. Measured in cycles per second(cycle/s) or s^-1. Also measured in hertz(Hz), defined as 1 cycle/s
Frequency is Directly Proportional to Speed at which Wave is Traveling The faster the wave, the more crests will pass a fixed location per unit time. Frequency is inversely proportional to the wavelength(λ) - the farther apart the crests, the fewer that will pass a fixed location per unit time
Frequency Equation v = c/λ... Where c = 3.00 x 10^8 ms^-1(speed of light)
Electromagnetic Spectrum Includes all wavelengths of electromagnetic radiation. Short wavelength light inherently has greater energy than long wavelength light
Gamma(γ) Ray The form of electromagnetic radiation with the shortest wavelength. This is the light produced by the sun, other stars, and certain unstable atomic nuclei on Earth
X-rays Have longer wavelengths than gamma rays. X-rays pass through many substances that block visible light and are therefore used to images bones and internal organs
Ultraviolet(UV) Radation The component of sunlight that produces a sunburn
Visible Light Ranging from violet(shorter wavelength, higher energy) to red(longer wavelength, lower energy)... Violet-Blue-Green-Yellow-Orange-Red(VBGYOR). Ranges from 400nm - 750nm
Infrared(IR) Radiation The heat you feel when you place your hand near a hot object is infrared radiation
Microwaves Used for radar and in microwave ovens
Radio Waves Used to transmit the signals responsible for AM and FM radio, cellular telephone, television, and other forms of communication
Electromagnetic Spectrum with 1. Increasing wavelength(λ).. 2. Decreasing Frequency(v).. 3. Decreasing Energy(E) Gamma(γ) Ray --> X-ray --> Ultraviolet(UV) Radiation --> Visible Light(VBGYOR) --> Infrared(IR Radiation --> Microwave --> Radio(FM --> AM)
Interference The way that waves interact with each other in a characteristic way: they cancel each other out or build each other up, depending on their alignment upon interaction.
Constructive Interference IF two waves of equal amplitude are in phase when they interact-that is, they align with overlapping crests - a wave with twice the amplitude results
Destructive Interference If two waves are completely out of phase when they interact - that is, they align so that the crest from one source overlaps with the trough from the other source - the waves cancel
Diffraction When a wave encounters an obstacle or a slit that is comparable in size to its wavelength, it bends(or diffracts) around it
Photoelectric Effect The observation that many metals emit electrons when light shines upon them.. a. when sufficiently energetic light shines on a metal surface, the surface emits electrons.. b. The emitted electrons can be measured as an electrical current
Einstein's Proposal for Photoelectric Effect Light energy must come in packets. The amount of energy(E) in a light packet depends on its frequency(v) according to the following equation: Ephoton = hv... where h, called Planck's constant, has the value h = 6.626 x 10^-34J*s
Photon or Quantum of Light A packet of light
Energy of Photon Expressed in Terms of Wavelength E = hc/λ... The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength
Threshold Frequency Condition hv = Φ... With h as Plank's constant, v as the energy of photon, and Φ as binding energy of emitted electron
Kinetic Energy(KE) of Ejected Electron The difference between the energy of the photon(hv) and the binding energy of the electron, as given by the equation: KE = hv - Φ
Atomic Spectroscopy The study of the electromagnetic radiation absorbed and emitted by atoms
Emission Spectrum(Atomic Spectrum) The range of wavelengths emitted by a particular element, used to identify the element
Bohr Model Electrons travel around the nucleus in circular orbits which exist only at specific, fixed distances from the nucleus with energy levels that are fixed or quantized. Bohr called these orbits stationary states.
Bohr Model and Emission Spectra(Atomic Spectrum) No radiation is emitted by an electron orbiting the nucleus in a stationary state. It is only when an electron jumps, or makes a transition, from one stationary state to another that radiation is emitted or absorbed.
Spectral Line According to the Bohr model, each spectral line is produced when an electron falls from one stable orbit, of stationary state, to another of lower energy
de Broglie Relation The wavelength (λ) of an electron of mass m moving at velocity v is given by... λ = h/mv... Wavelength is inversely proportional to its momentum
Complementary Properties Exclude one another-the more we know about one, the less we know about the other. The wave nature and particle nature of the electron are complementary properties
Heisenberg's Uncertainty Principle Equation Îx * mÎv >or= h/4pi... where Îx is the uncertainty in the position, Îv is the uncertainty in the velocity, m is the mass of the particle, and h is Planck's constant
Heisenberg's Uncertainty Principle States that the product of Δx and mΔv must be greater than or equal to a finite number(h/4pi). The more accurately you know the position of an electron(the smaller Δx) the less accurately you can know its velocity(the bigger Δv) and vice vera.
Complementarity of Wave and Particle Nature Our inability to observe electrons simultaneously as wave and particle means we cannot simultaneously measure its position and velocity. Complementarity of the wave and particle nature of electrons results in complementarity of velocity and position
Deterministic The present determines the future. Newton's laws of motion are deterministic
Indeterminancy The principle that present circumstances do not necessarily determine future events in the quantum-mechanical realm
Orbital A probability distribution map showing where the electron is likely to be found. The highest probability in which an electron is located
Quantum Numbers(n) 1. Principal Quantum Number(n)... 2. Angular Momentum Quantum Number(l)... 3. Magnetic Quantum Number(ml)... 4. Spin Quantum Number(ms)
Principle Quantum Number(n) The principal quantum number is an integer that determines the overall size and energy of an orbital. Possible values are n = 1, 2, 3, ... and so on.
Energy of Orbital Equation En = -2.18 x 10^-18J(1/n^2).... (n = 1, 2, 3, ...)... Orbitals with higher values of n have greater(less negative) energies. As n increase, the spacing between the energy levels becomes smaller
Angular Momentum Quantum Number(l) An integer that determines the shape of the orbital. Possible values for l are l = 0, 1, 2, ... , (n-1). In other words, for a given values of n, l can be any integer(including 0) up to n-1
Letters Designated for Values of l l = 0(s).. l = 1(p).. l = 2(d).. l = 3(f)
Letter Designation for l = 0 s
Letter Designation for l = 1 p
Letter Designation for l = 2 d
Letter Designation for l = 3 f
Magnetic Quantum Number(ml) An integer that specifies the orientation of the orbital. Possible values of ml are the integer values(including zero) ranging from -l(-angular momentum quantum number) to +l(+ angular momentum quantum number)
Spin Quantum Number(ms) An integer that specifies the orientation of the spin of the electron. The orientation of the electron's spin is quantized, with only two possibilities: that we can call spin up(ms = +1/2) and spin down(ms = -1/2). Each orbital can hold two electrons
Principal Level(Principal Shell) Orbitals with the same value of n(same overall size and energy) are said to be in the same principal level
Sublevel(Subshell) Orbitals with the same values of n(same overall shape and energy) and l(same shape) are said to be in the same sublevel
1. Quantum Number Relationships The number of sublevels in any level is equal to n, the principal quantum number. Therefore, the n = 1 level has one sublevel, the n = 2 level has two sublevels, etc.
2. Quantum Number Relationships The number of orbitals in any sublevel is equal to 2l + 1. Therefore, the s sublevel(l = 0) has one orbital, the p sublevel(l = 1) has three orbitals, the d sublevel(l = 2) has five orbitals, etc.
3. Quantum Number Relationships The number of orbitals in a level is equal to n^2. Therefore, the n = 1 level has one orbital, the n = 2 level has four orbitals, the n = 3 level has nine orbitals, etc.
Excitation When an atom absorbs energy, an electron at a lower energy orbital is excited or promoted to a higher energy orbital
Emission(Radiation) When an electron falls back or relaxes to a lower energy level. As it does, it releases a photon of light containing an amount of energy precisely equal to the energy difference between the two energy levels
Calculating the Change in Energy When an Electron Transitions ΔE = -2.18 x 10^-18 J((1/nf^2)-(1/ni^2))
Relationship Between Energy Change in Atom and Photon Emmited The exact amount of energy emitted by the atom is carried away by the photon: ΔEatom = -Ephoton
Probability Density The probability(per unit volume) of finding the electron at a point in space... ψ^2 = probability density = probability/unit volume
Radial Distribution Function Represents the total probability of finding the electron within a thin spherical shell at a distance r from the nucleus
Equation for Total Radial Probability(at a given r) Total Radial Probability(at a given r) = (probability/unit volume) x volume of shell at r
Node A node is a point where the wave function(ψ), and therefore the probability density(ψ^2) and radial distribution function, all go through zero
Phase The sign of the amplitude of a wave(positive or negative)
Created by: TimChemistry1